4[formula omitted] AdS Einstein–Gauss–Bonnet black hole endowed with Lorentzian noncommutativity: [formula omitted] criticality, Joule–Thomson expansion, and shadow

Abstract

In this article, we get a static, spherically symmetric 4D-AdS EGB black hole inspired by noncommutative geometry, where noncommutativity is expressed by a Lorentzian distribution. The noncommutativity correction has changed the relevant thermodynamic quantities. The cosmological constant Λ is interpreted as a dynamical pressure, and the noncommutative parameter Θ is treated as a thermodynamic variable to keep the first thermodynamic law and the Smarr formula in place. Our solution’s P−v criticality was investigated in the extended phase space, where the large/small black hole phase transition arises for the noncommutative 4D-AdS EGB black hole. That is, the noncommutativity parameter influences the phase transition as well as the critical pressure, horizon radius, and temperature; as a result, the critical ratio is also influenced and does not yet remain universal, as in the Van der Waals systems. The Joule–Thomson expansion has been studied in extended phase space. We acquired the inversion points (Pi,Ti) as a function of Θ, which allowed us to analyze the isenthalpic and inversion curves in the T−P plane and demonstrate the cooling and heating zones. In addition, it has been shown that the shadow radius is reduced when we increase the noncommutativity parameter, as is the peak of the associated energy emission rate, which decreases with the rise of the parameter Θ.